I am working on my aerospace engineering dissertation for active damping of wind turbine vibration. The problem I have here is to do with strucures/mechanics.
I am trying to find the centroid of an arbitrary aerofoil section, but it has been at least a year since I found the centroid of anything, and I am slighlty confused. The method I used gave a result that looks wrong
I have a polynomial expression that describes the shape of the section. Let's just say that y=f(x).
I know to find the centroid with respect to x you use the double integral: Qx=int(y)dA=int(y)dxdy. but
I can easily integrate w.r.t. x, but because y is a funtion of x, and y is not constant like a rectangle would be, I don't really know what to do.
I tried multiplying the integral with respect to x and then multiplying by the maximum thickness (in the y-direction) of the aerofoil. This gave a result that ooks far too big to be accurate.
I could use the trapezium rule, adding rectangles and triangles to approximate the profile, but do not really want to loose any accuracy if at all possible.
I'm not really sure how to define dy. Is it just the y-ordinate at a given x? Something tells me that at a given x, y>>dy.
If anybody can point me in the right direction or tell me